The purpose of this paper is to establish that for any compact, connected
C^{\infty} Riemannian manifold there exists a robust family of kernels of
increasing smoothness that are well suited for interpolation. They generate
Lagrange functions that are uniformly bounded and decay away from their center
at an exponential rate. An immediate corollary is that the corresponding
Lebesgue constant will be uniformly bounded with a constant whose only
dependence on the set of data sites is reflected in the mesh ratio, which
measures the uniformity of the data.